Gas Turbines Part 6 docx

Gas Turbines 114 Lowest temperature limit of gas turbine outlet T Φ / T relationship before Δ F Φ / T relationship after Δ F HI before Δ F HI after Δ F Cogeneration before Δ F Cogeneration after Δ F Φ Fig. 5. The simplified temperature/heat flow rate (T/ Φ ) diagram before and after changing the flow rate (ΔF) of the raw material: performing heat integration (HI), and cogeneration before and after ΔF. • molar heat capacity (C m ) • amount flow rate (F) The inlet temperature (T tur,in ) is kept constant. The thermodynamic efficiency of the medium pressure turbine ( η tur ) and the mechanical efficiency of the generator ( η gen ) is supposed to be 85 % for each. The annual depreciation of the medium pressure turbine (C d,tur in EUR/a) is a function of the power (P tur ; Biegler et al., 1997): C d, tur = (22 946 + 13.5 ⋅ P tur ) ⋅ 4 (10) The published cost equations for the equipment are not usually adjusted to the real, higher industrial costs, therefore, the costs are multiplied by a factor (4), determined by experience. 3.3 Heat exchanger (H) The residual heat in the heat exchanger (H) can usefully be applied to the heat integration. The heat flow ( Φ ) can be calculated with known inlet (T in H ) and outlet temperatures (T out H ), by using equation 11: (T in H − T out H ) ⋅ CF H = Φ H (11) where CF H is the heat capacity flow rate of the stream in heat exchanger. Electricity Cogeneration using an Open Gas Turbine 115 3.4 Separator (S) The separator has the task of separating liquid from the vapour phase. The product is in liquid phase. Vapour flow is compressed in the compressor (C). The balanced amounts of the separation for all the components (s = 1 S) are: F in = F out,v + F out,l (12) F in ·x in s = F out,v ·x out,v s + F out,l ·x out,l s s = 1, …, S (13) S out,v s s 1x = Σ (14) S out,l s s 1x = Σ (15) K s = d s + c s ⋅ T out + b s ⋅ (T out ) 2 s = 1, …, S (16) where d s , c s and b s are equilibrium constants during separation x out,v s = K s ⋅ x out,l s s = 1, …, S (17) The inlet amount flow rate for separation (F in ) is the sum of the outlet amounts flow rates of the vapour (F out,v ) and liquid phases (F out,l ; see Equation 12). Equation 13 includes the amount flow fractions. x is the amount fraction in vapour (v) or liquid phase (l). The equilibrium constant (K) of the s th component during separation is a function of temperature (see Equation 16). 3.5 Compressor (C) Vapour flow from the separator is compressed within the compressor (C). The temperatures at the outlets of the compressor (T out c ; depend on the inlet temperatures (T in c ), and can be calculated by the equation: T out c = a c + b c ⋅ T in c (18) where a c and b c are the temperature constants for polytropic compression. Once we know, the whole model of the open gas turbine system can be optimized, using different methods. 4. Case study The suggested open gas turbine system was tested in an existing complex, low-pressure Lurgi methanol plant producing crude methanol by using nonlinear programming (NLP; Biegler et al., 1997). The parameters in the model of an open gas turbine were simultaneously optimized using the GAMS/MINOS (Brooke at al.; 1992). This NLP can be solved using a large-scale reduced gradient method (e. g. MINOS). The model is non- convex, it does not guarantee a global optimization solution but it quickly gives good results for non-trivial, complex processes. The NLP model contains variables of all those process’ Gas Turbines 116 parameters: molar heat capacities, material flow rates, heat flow rates, and temperatures, which are limited by real constraints. 4.1 Results The simultaneous NLP of heat and power integration, and the optimization selected for electricity generation using a gas turbine pressure drop from 49.7 bar to 35 bar with an outlet temperature of T tur, out = 110 o C (Fig. 6). This structure enables the generation of 12.7 MW of electricity. The steam exchanger (HEST) needs 16.5 MW of heat flow rate. The integrated process streams in HEPR, exchange 3.6 MW of heat flow rate. The power of the first and the second compressors are 2.0 MW and 2.8 MW, respectively. The HEW1 exchanges 2.0 MW. Within the heat exchangers, HEW and HEA 7.1 MW and 4.7 MW of heat flow rate are exchanged with the existing areas, respectively, when cooling. The additional annual of methanol production is 0.75 mol/s, purge gas outlet flow rate is decreased from 210 mol/s to 190 mol/s. HEW1 COMP2 COMP1 HEW HEA SEP TUR REA HEST HEPR 51 bar 41 bar 35 bar 35 bar 35 bar airC.W. crude methanol purge 3.6 MW of heat exchange new heat exchanger 16.5 MW of high pressure steam 12.7 MW of electricity cogeneration 110 o C 0.75 mol/s of aditional methanol production decreasing purge gas flow rate to 190 mol/s new two-stage compressor 2.8 MW 2 MW 49.5 bar Fig. 6. Optimised flow sheet for crude methanol production, using a open gas turbine system Electricity Cogeneration using an Open Gas Turbine 117 The additional annual depreciation of the gas turbine, new heat exchangers (HEST, HEW1, having areas of 527 m 2 and 324 m 2 ), and the new two-stage compressor, is 2 040 kEUR/a (Table 1). The cost of the high pressure steam used in HEST is 1 750 kEUR/a. In the depreciation account for retrofit, we included additional costs to the new units only: 30 kEUR/a for the instrumentation cost (which is estimated to be 15 % of the additional direct plant cost), 10 kEUR/a for the contingency (estimated at 5 % of the additional direct plant cost), 4 kEUR/a for the maintenance cost (estimated as 2 % of the additional direct plant cost), and 15 kEUR/a for the turbine down time (estimated as 5 % of the additional plant direct cost). The additional annual income of the electricity produced is 5 530 kEUR/a. The additional annual income of the methanol produced is 79 kEUR/a. The additional profit from process and power integration is estimated to be 1 760 kEUR/a for the modified process. Installed cost of heat exchanger * /EUR: (8 600 + 670 A 0,83 ) ⋅ 3.5 ⋅ 2 # Installed cost of compressor, C com & /EUR: 2 605 ⋅ P 0,82 Installed cost of gas turbine, C tur & /(EUR/a): (22 946 + 13.5 P tur ) ⋅ 4 # Price of methanol (C M ) + /(EUR/t): 115.0 Price of electricity (C el ) ** /(EUR/(kW ⋅ a)): 435.4 Cost of 37 bar steam (C 37 ) ** /(EUR/(kW ⋅ a)): 106.3 Cost of cooling water (C CW ) ** /(EUR/(kW ⋅ a)): 6.2 * Tjoe and Linnhoff, 1986; A = area in m 2 ** Swaney, 1989 & Biegler et al., 1997; P = power in kW + ten years average # published cost equations for the equipment are adjusted to the real, higher industrial costs using multipliers (2 or 4). Table 1. Cost items for example process 7. Conclusion The inclusion of open gas turbine can increase the operating efficiency of the process. The gas turbine with its pressure and temperature drop can be included in the process cycle. The working fluid comes from the reactor and circulates through the process units: gas turbine, heat exchanger, separator (where the liquid product separates), and the compressor. 8. References Biegler, L. T.; Grossmann, I. E. & Westerberg, A. W. (1997). Systematic methods of chemical process design, Prentice Hall, Upper Saddle River, New Jersey, 1−408. Brooke, A.; Kendrick D. & Meeraus, A. (1992). GAMS: A User’s Guide, Palo Alto, Scientific Press. Gas Turbines 118 Smith, J.M. & Van Ness, H.C. (1987). Introduction to chemical engineering thermodynamics, McGraw-Hill, New York, 496−518. Swaney, R. (1989). Thermal integration of processes with heat engines and heat pumps, AIChE Journal 35/6, pp. 1010. Tjoe, T. N. & Linnhoff, B. (1986). Using pinch tehnology for process retrofit. Chem. Engng 28 47−60. 6 Gas Turbine Condition Monitoring and Diagnostics Igor Loboda National Polytechnic Institute Mexico 1. Introduction Gas turbine monitoring and diagnostics belong to a common area of condition monitoring (health monitoring) of machinery and mechanical equipment such as spacecrafts, aircrafts, shipboard systems, various power plants and industrial and manufacturing processes. They can be considered as complex engineering systems and become more sophisticated during their further development that results in potential degradation of system reliability. In order to keep reliability high, various diagnostic tools are applied. Being capable to detect and identify incipient faults, they reduce the rate of gross failures. Considerable increase of industrial accidents and disasters has been observed in the last decades (Rao, 1996). Mechanical failures cause a considerable percentage of such accidents. Various deterioration factors can be responsible for these failures. Among them, the most common factors that degrade a healthy condition of machines are vibration, shock, noise, heat, cold, dust, corrosion, humidity, rain, oil debris, flow, pressure, and speed (Rao, 1996). In these conditions, health monitoring has become an important and rapidly developing discipline which allows effective machines maintenance. In two last decades the development of monitoring tools has been accelerated by advances in information technology, particularly, in instrumentation, communication techniques, and computer technology. Modern sensors trend to preliminary signal processing (filtering, compressing, etc.) in order to realize self-diagnostics, reduce measurement errors, and decrease volume of data for subsequent processing. So, sensors become more and more “intelligent” or “smart”. Development of communication techniques, in particular, wireless technologies drastically simplifies data acquisition in the sites of machine operation. Data transmission to centralized diagnostic centres is also accelerated. In these centres great volume of data can effectively be analyzed by qualified personnel. The personal computer has radically changed as well. Large numbers of powerful PCs united in networks allow easy sharing the measured data through the company, fast data processing, and suitable access to the diagnostic results. Development of the PC technology also allows many independent disciplines to be integrated in condition monitoring. Success of monitoring not only depends on perfection of monitoring hardware and software themselves, but also is determined by tight monitoring integration with maintenance when the both disciplines can be considered as one multidiscipline. Behind this trend lies a well Gas Turbines 120 known concept of Condition Based Maintenance (CBM) as well as ideas of Condition Monitoring and Diagnostic Engineering Management (COMADEM) (Rao, 1996) and Prognostics and Health Management (PHM) (Vachtsevanos et al., 2006). As illustrated by many examples in (Rao, 1996), the proper organization of the total monitoring and maintenance process can bring substantial economical benefits. Numerous engineering systems, which considerably differ in nature and principles of operation, need individual techniques in order to realize effective monitoring. The variety of known monitoring techniques can be divided into five common groups: vibration monitoring, wear debris analysis, visual inspection, noise monitoring, and environment pollution monitoring (Rao, 1996). The two first approaches are typical for monitoring rotating machinery, including gas turbines. A gas turbine engine can be considered as a very complex and expensive machine. For example, total number of pieces in principal engine components and subsystems can reach 20,000 and more; heavy duty turbines cost many millions of dollars. This price can be considered only as potential direct losses due to a possible gas turbine failure. Indirect losses will be much greater. That is why, it is of vital importance that the gas turbine be provided by an effective monitoring system. Gas turbine monitoring systems are based on measured and recorded variables and signals. Such systems do not need engine shutdown and disassembly. They operate in real time and provide diagnostic on-line analysis and recording data in special diagnostic databases. With these databases more profound off-line analysis is performed later. The system should use all information available for a diagnosed gas turbine and cover a maximal number of its subsystems. Although theoretical bases for diagnosis of different engine systems can be common, each of them requires its own diagnostic algorithms taking into account system peculiarities. Nowadays parametric diagnostics encompasses all main gas turbine subsystems such as gas path, transmission, hot part constructional elements, measurement system, fuel system, oil system, control system, starting system, and compressor variable geometry system. In order to perform complete and effective diagnosis, different approaches are used for these systems. In particular, the application of such common approaches of rotating machinery monitoring as vibration analysis and oil debris monitoring has become a standard practice for gas turbines. However, the monitoring system always includes another technique, which is specific for gas turbines, namely gas path analysis (GPA). Its algorithms are based on a well-developed gas turbine theory and gas path measurements (pressures, temperatures, rotation speeds, and fuel consumption, among others). The GPA can be considered as a principal part of a gas turbine monitoring system. The gas path analysis has been chosen as a representative approach to the gas turbine diagnosis and will be addressed further in this chapter. However, the observations made in the chapter may be useful for other diagnostic approaches. The gas path analysis provides a deep insight into gas turbine components’ performances, revealing gradual degradation mechanisms and abrupt faults. Besides these gas path defects, malfunctions of measurement and control systems can also be detected and identified. Additionally, the GPA allows estimating main engine performances that are not measured like shaft power, thrust, overall engine efficiency, specific fuel consumption, and compressor surge margin. Important engine health indicators, the deviations in measured variables induced by engine deterioration and faults, can be computed as well. Gas Turbine Condition Monitoring and Diagnostics 121 The gas path analysis is an area of extensive studies and thousands of technical papers can be found in this area. Some common observations that follow from these works and help to explain the structure of this chapter are given below. First, it can be stated that gas turbine simulation is an integral part of the diagnostic process. The models fulfil here two general functions. One of them is to give a gas turbine performance baseline in order to calculate differences between current measurements and such a baseline. These differences (or deviations) serve as reliable degradation indices. The second function is related to fault simulation. Recorded data rarely suffice to form a representative classification because of the rare and occasional appearance of real faults and very high costs of real fault simulation on a test bed. That is why mathematical models are involved. The models connect degradation mechanisms with gas path variables, assisting in this way with a fault classification that is necessary for fault diagnosis. Second, a total diagnostic process can be divided into three general and interrelated stages: common engine health monitoring (fault detection), detailed diagnostics (fault identification), and prognostics (prediction of remaining engine life). Since input data should be as exact as possible, an important preliminary stage of data validation precedes these principal diagnostic stages. In addition to data filtration and averaging, it also includes a procedure of computing the deviations, which are used practically in all methods of monitoring, diagnostics, and prognostics. Third, gas turbine diagnostic methods can be divided into two general approaches. The first approach employs system identification techniques and, in general, so called thermodynamic model. The used models relate monitored gas path variables with special fault parameters that allow simulating engine components degradation. The goal of gas turbine identification is to find such fault parameters that minimize difference between the model-generated and measured monitored variables. The simplification of the diagnostic process is achieved because the determined parameters contain information on the current technical state of each component. The main limitation of this approach is that model inaccuracy causes elevated errors in estimated fault parameters. The second approach is based on the pattern recognition theory and mostly uses data-driven models. The necessary fault classification can be composed in the form of patterns obtained for every fault class from real data. Since patterns of each fault class are available, a data-driven recognition technique, for example, neural network, can be easily trained without detailed knowledge of the system. That is why, this approach has a theoretical possibility to exclude the model (and the related inaccuracy) from the diagnostic process. Fourth, the models used in condition monitoring and, in particular, in the GPA can be divided into two categories – physics-based and data-driven. The physics-based model (for instance, thermodynamic model) requires detailed knowledge of the system under analysis (gas turbine) and generally presents more or less complex software. The data-driven model gives a relationship between input and output variables that can be obtained on the basis of available real data without the need of system knowledge. Diagnostic techniques can be classified in the same manner as physics-based or model-based and data-driven or empirical. Illustrating the above observations, Fig. 1 presents a classification of gas path analysis methods. Taking into the account the observations and the classification, the following topics will be considered below: real input data for diagnosis, mathematical models involved, preliminary data treatment, fault recognition methods and accuracy, diagnosis and monitoring interaction, and application of system identification methods for fault diagnosis. Gas Turbines 122 Fig. 1. Classification of gas path analysis techniques 2. Diagnostic models 2.1 Nonlinear static model In the GPA the physics-based models are presented by thermodynamic models for simulating gas turbine steady states (nonlinear static model) and transients (nonlinear dynamic model). Since the studies of Saravanamuttoo et al., in particular, (Saravanamuttoo & MacIsaac, 1983), application of the thermodynamic model for steady states has become common practice and now this model holds a central position in the GPA. Such a model includes full successive description of all gas path components such as input device, compressor, combustion chamber, turbine, and output device. Such models can also be classified as non-linear, one-dimensional, and component-based. The thermodynamic model computes a (m×1)-vector Y G of gas path monitored variables as a function of a vector U G of steady operational conditions (control variables and ambient conditions) as well as a (r×1)-vector Θ G of fault parameters, which can also be named health parameters or correction factors depending on the addressing problems. Given the above explanation, the thermodynamic model has the following structure: (,)YFU →→→ = Θ . (1) There are various types of real gas turbine deterioration and faults such as fouling, tip rubs, seal wear, erosion, and foreign object damage whose detailed description can be found, for example, in the study (Meher-Homji et al., 2001). Since such real defects occur rarely during maintenance, the thermodynamic model is a unique technique to create necessary class descriptions. To take into account the component performance changes induced by real GPA techniques Stages of diagnostic process Theoretical bases Models used D ata validation, d eviations Monitorin g Dia g nostics Pro g nostics System identification Pattern recognition Physics -based Data -driven Gas Turbine Condition Monitoring and Diagnostics 123 gradual deterioration mechanisms and abrupt faults, the model includes special fault parameters that are capable to shift a little the components’ maps. Mathematically, the model is a system of nonlinear algebraic equations reflecting mass, heat, and energy balance for all components operating under stationary conditions. The thermodynamic model represents complex software. The number of algebraic equations can reach 15 and more and the software includes dozens of subprograms. The most of the subprograms can be designed as universal modules independent of a simulated gas turbine, thus simplifying model creation for a new engine. System identification techniques can significantly enhance model accuracy. The dependency 1 ()YfU= G G realized by the model can be well fitted and simulation errors can be lowered up to a half per cent. Unfortunately, it is much more difficult to make more accurate the other dependency 2 ()Yf=Θ G G because faults rarely occur. The study presented in (Loboda & Yepifanov, 2010) shows that differences between real and simulated faults can be visible. As mentioned before, the thermodynamic model for steady states has wide application in gas turbine diagnostics. First, this model is used to describe particular faults or complete fault classification (Loboda et al., 2007). Second, the thermodynamic model is an integral part of numerous diagnostic algorithms based on system identification such as described in (Pinelli & Spina, 2002). Third, this nonlinear model allows computing simpler models (Sampath & Singh, 2006), like a linear model (Kamboukos & Mathioudakis 2005) described below. 2.2 Linear static model The linear static model present linearization of nonlinear dependency 2 ()Yf = Θ G G between gas path variables and fault parameters determined for a fixed operating condition U G . The model is given by a vectorial expression YH δ δ = Θ G G . (2) It connects a vector δ Θ G of small relative changes of the fault parameters with a vector Y δ G of the corresponding relative deviations of the monitored variables by a matrix H of influence coefficients (influence matrix). Since linearization errors are not too great, about some percent, the linear model can be successfully applied for fault simulation at any fixed operating point. However, when it is used for estimating fault parameters by system identification methods like in study (Kamboukos & Mathioudakis, 2005), estimation errors can be significant. Given the simplicity of the linear model and its utility for analytical analysis of complex diagnostic issues, we can conclude that this model will remain important in gas turbine diagnostics. The matrix H can be easily computed by means of the thermodynamic model. The gas path variables Y G are firstly calculated by the model for nominal fault parameters 0 Θ G . Then, small variations are introduced by turns in fault parameters and the calculation of the variables Y G is repeated for each corrected parameter. Finally, for each pair i Y and j Θ the corresponding influence coefficient is obtained by the following expression 00 0 0 () () () i j i jj i ij j j i YY Y H Y δ δ Θ −Θ Θ−Θ == Θ Θ Θ G G G . (3) [...]... 0.09 0.08 0.12 0.10 0.12 0.08 0.35 0.14 0.17 0.11 PC 0.07 0.11 0.74 0.15 0. 36 0.19 1.42 PТ 0.08 0.11 0 .66 0. 16 0.33 0.21 1 .69 Gf 0.13 0.17 0.18 0. 16 0. 86 0. 36 1.01 TC 0.12 0.11 0.45 0.92 0 .67 0. 26 1.41 nhp 0.39 0.13 0.17 0.19 0.31 0.27 0.25 Nе 0.17 0.15 1.20 6. 11 0.51 1.10 0.29 - mean 0.108 0.127 0.141 0.143 0.157 0. 167 0.2 16 0.224 Table 1 Deviation errors for different arguments In all described above... class types The 138 Gas Turbines mean probability Pe also rises just a little, by about 0.5%, in the row "Gen." So the diagnosis reliability losses resulting from the classification generalization are insignificant → Classification Conv Gen Pe ΔAc 0. 166 0.1 56 Δηc 0. 266 0.275 ΔAhpt 0.132 0.131 Δηhpt 0. 265 0. 269 ΔApt 0.1 46 0.148 Δηpt 0.172 0.190 Δσcc 0.154 0. 161 Δηcc 0.174 0.184 Δσin 0. 168 0.180 Pe 0.1827... Θ , t ) (4) A separate influence of time variable t is explained by inertia nature of gas turbine dynamic processes, in particular, by inertia moments of gas turbine rotors The gas path parameters Y of the model (4) are computed numerically as a solution of the system of differential equations in which the right parts are calculated from a system of algebraic equations reflecting the conditions of... addition to the MLP described above, some other network types are also used in the gas path analysis, in particular, Radial Basis Networks, Probabilistic Neural Networks (Romessis & Mathioudakis, 2003; Romessis et al., 2007), and Bayesian Belief Networks (Romessis & Mathioudakis, 20 06; Romessis et al., 2007) Foundations of these particular recognition and approximation tools can be found in any book in the... that in most cases networks are employed for gas turbine fault identification, in particular, to form fault classification (Ogaji et al., 2003) and to estimate fault parameters (Romessis & Mathioudakis, 20 06) However, the ANNs not only are applied for recognition problems, but they also are famous as good function approximators in many fields including gas turbine monitoring (Fast et al., 2009) In...124 Gas Turbines 2.3 Nonlinear dynamic model Although methods to diagnose at steady states are more developed and numerous than the methods for transients, current studies demonstrate growing interest in the gas turbine diagnosis during dynamic operation (Loboda et al., 2007; Ogaji et al., 2003) A thermodynamic gas path model (dynamic model) is therefore in... polynomial baseline model can be successfully used in real monitoring systems instead of neural networks At least, it seems to be true for simple cycle gas turbines with gradually changed performance, like the turbines considered in the study 135 Gas Turbine Condition Monitoring and Diagnostics Concluding section 3, we would like to note that the considered here stage of data validation and computing... d2 , , dq corresponds to the accepted classification ( 16) To make a diagnosis d, a method-dependent criterion R j = R( Z * , D j ) is introduced as a measure of membership of a current pattern Z * to class Dj To determine the functions R j = R(Z* , Dj ) , the learning set is used After calculating all values R j , j = 1,q , a decision rule 1 36 Gas Turbines d = dl if Rl = max( R1 , R2 , , Rq ) (17) is... GT1 chosen as a test case In these studies steady state operation is determined in the thermodynamic model by a fixed gas generator speed and standard ambient condition Eleven full and partload steady states are set by the following speeds: 10700, 1 060 0, …, 9800, 9700 rpm Six simulated gas path variables correspond to a standard measurement system of the GT1 The single type fault classification consists... variables and should not reflect individual random errors of every input and output Though the trained network is ready for practical use in a gas turbine diagnosis, an additional stage of network verification is mandatory There is a common statistical rule that 1 26 Gas Turbines a function determined on one portion of the random data should be tested on another Consequently, to verify the MLP determined on . and heat pumps, AIChE Journal 35 /6, pp. 1010. Tjoe, T. N. & Linnhoff, B. (19 86) . Using pinch tehnology for process retrofit. Chem. Engng 28 47 60 . 6 Gas Turbine Condition Monitoring. another technique, which is specific for gas turbines, namely gas path analysis (GPA). Its algorithms are based on a well-developed gas turbine theory and gas path measurements (pressures, temperatures,. 6. Optimised flow sheet for crude methanol production, using a open gas turbine system Electricity Cogeneration using an Open Gas Turbine 117 The additional annual depreciation of the gas